The joint law of the last zeros of Brownian motion and of its Levy transform

Authors
Donati-Martin, C Shi, Z Yor, M
Citation
C. Donati-martin et al., The joint law of the last zeros of Brownian motion and of its Levy transform, ERGOD TH DY, 20, 2000, pp. 709-725
Citations number
19
Categorie Soggetti
Mathematics
Journal title
ERGODIC THEORY AND DYNAMICAL SYSTEMS
ISSN journal
01433857 → ACNP
Volume
20
Year of publication
2000
Part
3
Pages
709 - 725
Database
ISI
SICI code
0143-3857(200006)20:<709:TJLOTL>2.0.ZU;2-S
Abstract
The joint study of functionals of a Brownian motion B and its Levy transfor m beta = \ B \ - L. where L is the local time of B at zero, is motivated by the conjectured ergodicity of the Levy transform. Here, we compute explicitly the covariance of the last zeros before time on e of B and B, which turns out to be strictly positive.